Classical Heisenberg antiferromagnet on a garnet lattice: a Monte Carlo simulation

We have studied a classical antiferromagnet on a garnet lattice by means of Monte Carlo simulations in an attempt to examine the role of geometrical frustration in Gadolinium Gallium Garnet, Gd3Ga5O12 (GGG). Low-temperature specific heat, magnetisation, susceptibility, the autocorrelation function A(t) and the neutron scattering function S(Q) have been calculated for several models including different types of magnetic interactions and with the presence of an external magnetic field applied along the principal symmetry axes. A model, which includes only nearest-neighbour exchange, J1, neither orders down to the lowest temperature nor does it show any tendency towards forming a short-range coplanar spin structure. This model, however, does demonstrate a magnetic field induced ordering below T ~ 0.01 J1. In order to reproduce the experimentally observed properties of GGG, the simulated model must include nearest neighbour exchange interactions and also dipolar forces. The presence of weak next-to-nearest exchange interactions is found to be insignificant. In zero field S(Q) exhibits diffuse magnetic scattering around positions in reciprocal space where antiferromagnetic Bragg peaks appear in an applied magnetic field.Comment: 8 pages, 8 figures, to appear in PRB (JAN 2001

Triangular Antiferromagnets

In this article we review the effects of magnetic frustation in the stacked triangular lattice. Frustration increases the degeneracy of the ground state, giving rise to different physics. In particular it leads to unique phase diagrams with multicritical points and novel critical phenomena. We describe the confrontation of theory and experiment for a number of systems with differing magnetic Hamiltonians; Heisenberg, Heisenberg with easy-axis anisotropy, Heisenberg with easy-plane anisotropy, Ising and singlet ground state. Interestingly each leads to different magnetic properties and phase diagrams. We also describe the effects of ferromagnetic, rather than antiferromagnetic, stacking and of small distortions of the triangular lattice.Comment: Review article, 36 pages, revtex, 19 figures in PS format, to appear in Can. J. Phy

The study of the extended Higgs boson sector within 2HDM model

Consideration of the latest experimental data on the searches for extended sector of Higgs bosons produced at the LHC at a center-of-mass energy of 13 TeV, allows for computer modeling of the properties of supersymmetric particles within 2HDM model. The experimental restrictions on model parameters accounted in FeynHiggs code that is implemented in SusHi program, gave us the possibility to calculate the cross sections and branching fractions for three mechanisms of production and decay of Higgs bosons: 1) pp$\rightarrow H\rightarrow\tau\tau$, 2) pp$\rightarrow A\rightarrow Zh\rightarrow llbb$, 3) pp$\rightarrow H\rightarrow hh\rightarrow bb\tau\tau$ at a center-of-mass energy of 14 TeV. The considered computer modelling make it possible to draw conclusions about the need to take into account the b-associated production process of Higgs bosons for fermionic decay channel at large values of tan$\beta$. Differential cross sections with respect to the Higgs transverse momentum $p_t$ and pseudorapidity $\eta$ are calculated and the peculiarities of the kinematics of the Higgs boson decay products are recognized.Comment: 18 pages, 14 figures, presented at XV Conference of High energy physics, Kharkov, 21-24 March, 201

On the Specification and Verification of Communication Protocols

The purpose of this paper is to consider the most complicated problem related to computer network design, and especially to the so-called "gateways": the definition and estimation of the logical correctness of protocols. While the simple terminal connection of a computer to a computer system necessitates only the emulation of the chosen terminal, the very complicated interconnection of several computer networks requires the definition and implementation of a whole hierarchy of protocols. Naturally, all the protocols of each level must be rigorously specified and carefully verified before being implemented into soft-, firm-, or hardware. In order to achieve this goal, a technique based on a top-down approach, involving stepwise refinement and verification of the protocol actions in various situations, is proposed in this paper. This technique requires the formalism of a special kind of Petri net: the Petri net with enabling predicates

Shape-dependence of transmission, reflection and absorption eigenvalue densities in disordered waveguides with dissipation

The universal bimodal distribution of transmission eigenvalues in lossless diffusive systems un- derpins such celebrated phenomena as universal conductance fluctuations, quantum shot noise in condensed matter physics and enhanced transmission in optics and acoustics. Here, we show that in the presence of absorption, density of the transmission eigenvalues depends on the confinement geometry of scattering media. Furthermore, in an asymmetric waveguide, densities of the reflection and absorption eigenvalues also depend of the side from which the waves are incident. With increas- ing absorpotion, the density of absorption eigenvalues transforms from single-peak to double-peak function. Our findings open a new avenue for coherent control of wave transmission, reflection and absorption in random media.Comment: 9 pages 8 figure

Investigation of the Heating Processes and Temperature Field of the Frequency-controlled Asynchronous Engine Based on Mathematical Models

The study of the temperature field of the engine for non-stationary modes is done. A numerical simulation of a non-stationary thermal process using dynamic EHD, the characteristic of the rate of rise of temperatures is done. An increase in the temperature of individual parts in the idle interval, when the power of heat release is significantly reduced, is established, and the reverse of the heat flow through the air gap is established. It is shown that the EHD method, in contrast to the FEM, is self-sufficient, which determines its practical value. In various parts of the speed control range in the implementation of various laws of regulation. At the same time, the main electrical, magnetic and additional losses associated with the fundamental voltage harmonics (FVH), and mechanical losses, as well as additional electrical and magnetic losses associated with the higher voltage harmonics, change. When using serial asynchronous engines as frequency-controlled. Permissible under the conditions of heating power is significantly reduced by the power of serial engines. Depending on the synchronous speed, the reduction is from 10 % to 20 %. Given the additional overheating due to higher voltage harmonics, as well as the deterioration of the cooling conditions when adjusting the rotational speed "down" from the nominal, it seems very relevant

Controlling stress state of a hoisting shaft frame in the context of specific freezing process

Purpose is to obtain regularities of a stress state of such multilayer system as neighbourhood rock mass – frozen soil – hoisting shaft frame in the process of numerical analysis to control a frame state with the selection of efficient parameters; thickness depending upon a specific frozen process specifically. Methods. Numerical analysis on the basis of a finite-element method has been implemented relying upon Pro Complex Structure CAD for Windows (SCAD) which made it possible to obtain stress state of a hoisting shaft frame and its interaction with ice-soil blocking as well as with neighbourhood rock mass soil. Findings. Hoisting shaft model has been developed. The model is based upon actual geometry and results of laboratory studies. Three blocking types (i.e. reinforced-concrete blocks, gray cast-iron tubbings, and modified gray cast-iron tubbings) and two soil types (i.e. sand and clayish soil at +8°С temperature) in terms of different freezing temperatures (i.e. (–2, –6 and –10°С) were analyzed numerically with the use of the SCAD. Results of the research have helped identify dependences concerning formation of a stress state of the multilayer neighbourhood rock mass – frozen soil – hoisting shaft frame system while varying properties of the listed types of a frame, neighbourhood rock mass, and ice-soil blocking. Regularities of the stressed state components deepening upon the frozen soil elasticity modulus, corresponding to its certain temperature, and elasticity modulus of a hoisting shaft frame have been obtained. The regularities connect changes in the stress of a hoisting shaft blocking in the context of specific freezing process. Originality. The obtained dependences of the stressed state of a hoisting shaft frame on the soil elasticity modulus and the material are composite spatial surfaces reflecting representatively the stressed state of such multilayer systems as neighbourhood rock mass – frozen soil – hoisting shaft frame. Practical implications. The regularities of the stressed state, determined for such multilayer systems as neighbourhood rock mass – frozen soil – hoisting shaft frame, make it possible to control stress components selecting rational geometry of a frame and its material or temperature cycle to freeze soils while applying the specific method.Мета. Отримання в ході чисельного аналізу закономірностей зміни напруженого стану багатошарової системи “ґрунт оточуючого масиву – заморожений ґрунт – оправа шахтного стовбуру” для управління напруженим станом оправи із підбором ефективних параметрів (наприклад, товщини) в залежності від параметрів спеціального способу заморожування. Методика. Застосовано чисельний аналіз на основі методу скінченних елементів, реалізований на базі професійного комплексу Structure CAD for Windows (SCAD), що дозволив отримати напружений стан оправи шахтного стовбуру із його взаємодією із льодоґрунтовим огородженням та ґрунтом оточуючого масиву. Результати. Створено модель шахтного стовбура, що побудована на основі реальних геометричних розмірів і результатів лабораторних досліджень. В ході чисельного аналізу із застосуванням SCAD досліджено три типи оправи (залізобетонні блоки, тюбінги з сірого чавуну та тюбінги з модифікованого сірого чавуну), два типи ґрунтів (пісок та суглинок при температурі +8°С) при різних температурах заморожування (–2, –6 і –10°С). Результати досліджень дозволили відшукати залежності формування напруженого стану багатошарової системи “ґрунт оточуючого масиву – заморожений ґрунт – оправа шахтного стовбуру” при варіації властивостей вказаних типів оправи, ґрунту оточуючого масиву та льодоґрунтового огородження. Отримано закономірності компонент напруженого стану від модуля пружності замороженого ґрунту, що відповідає певній його температурі, та модуля пружності оправи шахтного стовбуру. Дані закономірності пов’язують зміну напружень оправи шахтного стовбуру при спеціальному способі заморожування. Наукова новизна. Отримані залежності компонент напруженого стану оправи шахтного стовбуру від модулю пружності ґрунту та матеріалу є складними просторовими поверхнями, що репрезентативно відображають напружений стан багатошарової системи “ґрунт оточуючого масиву – заморожений ґрунт – оправа шахтного стовбуру”. Практична значимість. Закономірності напруженого стану, визначені для багатошарової системи “ґрунт оточуючого масиву – заморожений ґрунт – оправа шахтного стовбуру”, дозволяють управляти компонентами напружень, підбираючи раціональні геометричних параметри та матеріал оправи, або температуру циклу заморожування ґрунтів при застосуванні цього спеціального способу.Цель. Получение в ходе численного анализа закономерностей изменения напряженного состояния многослойной системы “ґрунт окружающего массива – замороженный грунт – оправа шахтного ствола” для управления напряженным состоянием оправы с подбором эффективных параметров (например, толщины) в зависимости от параметров специального способа замораживания. Методика. Применен численный анализ на основе метода конечных элементов, реализованный на базе про-профессионального комплекса Structure CAD for Windows (SCAD), позволивший получить напряженное состояние оправы шахтного ствола с его взаимодействием с льодоґрунтовым ограждением и грунтом окружающего массива. Результаты. Создана модель шахтного ствола, построенная на основе реальных геометрических размеров и результатов лабораторных исследований. В ходе численного анализа с применением SCAD исследованы три типа оправы (железобетонные блоки, тюбинги из серого чугуна и тюбинги из модифицированного серого чугуна), два типа грунтов (песок и суглинок при температуре +8°С) при различных температурах замораживания (–2, –6 и –10°С). Результаты исследований позволили отыскать зависимости формирования напряженного состояния многослойной системы “грунт окружающего массива – замороженный грунт – оправа шахтного ствола” при вариации свойств указанных типов оправы, грунта окружающей массива и льодоґрунтового ограждения. Получены закономерности компонент напряженного состояния от модуля упругости замороженного грунта, что соответствует определенной его температуре, и модуля упругости оправы шахтного ствола. Данные закономерности связывают изменение напряжений оправы шахтного ствола при специальном способе замораживания. Научная новизна. Полученные зависимости компонент напряженного состояния оправы шахтного ствола от модуля упругости грунта и материала являются сложными пространственными поверхностями, репрезентативно отражающие напряженное состояние многослойной системы “грунт окружающей массива – замороженный грунт – оправа шахтного ствола”. Практическая значимость. Закономерности напряженного состояния, определенные для многослойной системы “грунт окружающей массива – замороженный грунт – оправа шахтного ствола”, позволяют управлять компонентами напряжений, подбирая рациональные геометрические параметры и материал оправы, или температуру цикла замораживания грунтов при применении этого специального способа.The results of the study were obtained in the process of implementing the state-financed research Analytical regularities of a stress-strain state of frame of hoisting shafts while specific operation performing (official registration No. 0117U006810). The authors express thanks to S.M. Likhman, Chief Engineer of Kyivmetrobud PJSC, and M.V. Bilous, Candidate of Science and Director of a Ukrheodezmark being a subsidiary company of Kyivmetrobud PJSC for their counseling as for the specific method of soil freezing and selection of rational designs of a hoisting shaft

Magnetic properties of geometrically frustrated SrGd2O4

A study of the magnetic properties of the frustrated rare earth oxide SrGd2O4 has been completed using bulk property measurements of magnetization, susceptibility and specific heat on single crystal samples. Two zero-field phase transitions have been identified at 2.73 and 0.48 K. For the field, H, applied along the a and b axes, a single boundary is identified that delineates the transition from a low field, low temperature magnetically ordered regime to a high field, high temperature paramagnetic phase. Several field-induced transitions, however, have been observed with H || c. The measurements have been used to map out the magnetic phase diagram of SrGd2O4, suggesting that it is a complex system with several competing magnetic interactions. The low-temperature magnetic behavior of SrGd2O4 is very different compared to the other SrLn2O4 (Ln = Lanthanide) compounds, even though all of the SrLn2O4 compounds are isostructural, with the magnetic ions forming a low-dimensional lattice of zigzag chains that run along the c axis. The differences are likely to be due to the fact that in the ground state Gd3+ has zero orbital angular momentum and therefore the spin-orbit interactions, which are crucial for other SrLn2O4 compounds, can largely be neglected. Instead, given the relatively short Gd3+-Gd3+ distances in SrGd2O4, dipolar interactions must be taken into account for this antiferromagnet alongside the Heisenberg exchange terms.Comment: 10 pages, 9 figure